the advanced concept of small satellite integrated navigation system ...

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GPS & GLONASS constellation and user motion model User attitude simulator E tr S User ephemerise generator X tr Calculator of the "true" antennae system position in the inertial frame errors of system initialization ephemerise errors User "On-Board" Software E ref s re f X s X ref ant S E* s X* s X tr ΔX N S ant GPS & GLONASS ephemerise generator X tr N S Definition of the observed GPS & GLONASS satellites X tr O N S Simulator of the GPS & GLONASS navigational message ref X (-30) O N S Integration of the observed GPS & GLONASS satellites reference trajectories ref X (t) O N S Formation of the reference measurement results φ ref Calculator of the reference antennae system position in the inertial frame User attitude data processing algorithm OUTPUT DATA X tr O N S X tr set of measurement errors Formation of the "true" measurement results ant φ tr ref ref ρ , δρ User position & velocity data processing algorithm tr tr ρ , δρ Fig. 4 Simplified diagram of simulation instant using all the observed navigational satellites, are considered as a complete sample to be processed by the LMS method. As the result, it is not necessary to involve complete mathematical model of angular satellite motion in the attitude determination algorithm. The simplified diagram of simulation is given in Fig. 4. The following notations are used in this figure: X is the vector of «true» TUD satellite position and tr S velocity components in the absolute inertial frame (IF2000), E is the vector of «true» TUD satellite Euler angles, tr S tr X NS is the vector of «true» GLONASS and GPS satellites ephemerides, tr X ant is the vector of «true» antenna position in the IF2000 frame (see below in detail), tr X ONS is the vector of «true» observed navigational satellites (ONS) ephemerides, tr ρ is the vector of «true» pseudorange measurement results, obtained from the observed navigational satellites, tr δρ is the vector of «true» pseudorange rate measurement results, obtained from the observed navigational satellites, tr Φ is the vector of «true» carrier phase difference measurement results, calculated for the observed navigational satellites, ref X ONS is the vector of observed navigational satellites ephemerides, which corresponds to the navigational message, ref X NS is the vector of observed navigational satellites short term («reference») ephemerides, calculated by the satellite onboard computer, ref X S is the user «reference» state vector, calculated by the onboard computer bases on the previous estimations, ref E S is the vector of the «reference» satellite Euler angles, calculated by onboard computer based on the previous estimations and angular motion model, ref X ant is the vector of the «reference» antenna position in the IF2000, calculated by onboard computer, using ref ref XS and ES data, ref ref ref ρ , δρ , ϕ are corresponding reference measurement data, generated based on the corresponding reference vectors ref ref ref ref XS , Xant , ES , XONS . * * E S , XS are the vectors of estimations of the user attitude, position and velocity. tr tr tr To obtain the values of XS , ES , X NS , the most accurate and complete models of motion as well as high-accuracy integration method are used. Mathematical Models and Algorithms Let us emphasize, that for simulation of the considered navigation system one has to create the following mathematical models and algorithms: • GLONASS and GPS constellation model; • GLONASS and GPS satellite observability model; • user orbital and angular motion models; • navigational message and receiver antennae system models; • algorithm of user position and velocity determination; • algorithm of user attitude determination. All the mentioned models have been created, considering wide set of uncontrollable factors and errors, such as GLONASS and GPS ephemerides maintenance systematic errors caused by the errors of orbit determination of the navigation satellites by the
on-ground complex; pseudorange and pseudorange rate systematic and random measurement errors caused by ionosphere delay, receiver clock drift and internal receiver noise; carrier phase difference measurement systematic and random errors caused by multi-path phenomenon, receiver clock drift, internal receiver noise; systematic and random errors of system initialization caused by the errors of auxiliary sensors data. A recursive Bayes algorithm (a modification of Kalman filtering) or the Least Mean Square algorithm has been used for user position and velocity determination. The latter has been used also for the user attitude determination. As it was said above, two levels of the used models have been developed for simulation: the more accurate model and integration method for «true» ephemerides generation and simplified model and integration algorithm for simulation of both navigation messages and «onboard» short-term ephemerides generation. Mathematical model of the navigational satellites motion Firstly, let us pay attention to the «true» ephemerides generation technique. Below we turn our attention only to its main specific features. The mathematical model of «true» ephemerides generation considers influence of the following uncontrollable factors (disturbances): force resulting from the Earth oblateness according to Cunningham expansion 3 till the 8th order, force resulting from Sun and Moon gravitational influence, aerodynamic drag force, force resulting form the solar pressure. The highly accurate Dormand-Prince integration method 3 of the 5(4) order with automatically adjustable step has been used for computation GPS and GLONASS satellites «true» position and velocity, considering the above mentioned disturbances. To provide efficiency of obtained integration results utilization, one uses Chebyshev’s polynomial approximation technique 3 . The order of polynomial was accepted equal to 16 and approximation interval has been accepted equal to 1000 sec. The simplified model for simulation of both navigation messages and «onboard» short-term ephemerides generation (so called «reference» data) considers the force resulting from the Earth oblateness according to Cunningham expansion till the 2nd order and force resulting from Sun and Moon gravitational influence. The standard Runge-Kutta integration method of the 2/6 rule with fixed step was used for computation of GPS and GLONASS satellites «reference» position and velocity, considering the above mentioned disturbances. To utilize the obtained integration results for «reference» ephemerides generation Chebyshev’s polynomial approximation technique has been used as well. To simulate the error of ephemerides maintenance one uses «true» ephemerides, corresponding to the closest half an hour, «distorted» by the additive random vector with zero mathematical expectation and diagonal covariance matrix with the following r.m.s. values: σ r = σl = σn = 10m. ; σ 0 05m s, r � = σ� = σ l n� = . / where the r, l, n subscripts denote radial, tangential and normal directions correspondingly. Mathematical model of the user satellite motion Two levels of the models complexity have been used for simulation of the user motion: the more accurate models and integration method for «true» satellite position and velocity computation and simplified model and integration algorithm for the «reference» data generation by the «onboard» software. The highly accurate technique for the user position and velocity computation is the same as for the «true » GPS and GLONASS satellites ephemerides generation. To use the obtained integration results for the user «true» ephemerides generation one uses Chebyshev’s polynomial approximation technique. The order of polynomial is equal to 16 and approximation interval is equal to 500 sec. The simplified «onboard» user motion model for the «reference» data performing considers the force resulting from the Earth oblateness according to Cunningham expansion till the 2nd order and the aerodynamic drag force. The standard Runge-Kutta integration method of the 2/6 rule with fixed step is used for computation of the user «reference» position and velocity, considering the above mentioned disturbances. A priori data are used as initial conditions for the «onboard» equations of the user motion. Later the current estimations of position and velocity are used, when «User position and velocity data processing algorithm» unit is initialized. The simplest model of the user angular motion was accepted as the «onboard» one due to LMS algorithm utilization in the «User attitude data processing algorithm» unit, namely: ref ref Es = 0, Es = ( ϑ ψ γ) � , where υ, ψ, γ are pitch, yaw and roll correspondingly.
Page 1 and 2: INPE / ABCM 14th International Symp
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Page 7 and 8: All the obtained simulation results

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